Let H be a finite Hopf algebra with CH,H = C −1 H,H . The duality theorem is shown for H, i.e., (R#H)#H ∗̂ ∼= R ⊗ (H⊗̄H ) as algebras in C. Also, it is proved that the Drinfeld double (D(H), [b]) is a quasi-triangular Hopf algebra in C. 2000 Mathematics subject Classification: 16w30.

This paper introduces a composite iteration scheme for approximating a zero point of accretive operators in the framework of uniformly smooth Banach spaces and the reflexive Banach space which has a weak continuous duality map, respectively. Our results improve and extend results of Kim, Xu and some others. AMS Mathematics Subject Classification (1991): 54H25, 47H10

Let H be a finite Hopf algebra with CH,H = C −1 H,H . The duality theorem is shown for H, i.e., (R#H)#H ∗̂ ∼= R ⊗ (H⊗̄H ) as algebras in C. Also, it is proved that the Drinfeld double (D(H), [b]) is a quasi-triangular Hopf algebra in C. 2000 Mathematics subject Classification: 16w30.

What is quantum geometry? This question is becoming a popular leitmotiv in theoretical physics and in mathematics. Conformal field theory may catch a glimpse of the right answer. We review global aspects of the geometry of conformal fields, such as duality and mirror symmetry, and interpret them within Connes’ non-commutative geometry.

We construct geometric examples of pseudomanifolds that satisfy the Witt condition for intersection homology Poincaré duality with respect to certain fields but not others. We also compute the bordism theory of K-Witt spaces for an arbitrary field K, extending results of Siegel for K = Q. 2000 Mathematics Subject Classification: 55N33, 57Q20, 57N80

A fundamental problem in spoken language is the duality between the continuous aspects of phonetic performance and the discrete aspects of phonological competence. We study a specific instance of this problem in Hungarian vowel harmony. We present a model where continuous phonetic distinctions uncovered by our experiments are linked to the discreteness of phonological form using the mathematics...

The duality proof of sampling localization given by Loy, Newbury, Anderssen and Davies in 2001 contains an oversight, as the classes of functions chosen do not assume the compact support. Here, it is shown how a minor change to the argument there yields a precise conclusion. 2000 Mathematics subject classification: 76A05, 46F12, 65R32.

Uncertainty theory is a branch of axiomatic mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. In uncertainty theory this paper proposes a definition of quadratic cross entropy and the principle of minimum quadratic cross entropy. Based on the principle, an application in statistics and a numerical algorithm to estimate uncertain dis...

*Correspondence: [email protected] 1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia 2Permanent address: Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India Full list of author information is available at the end of the article Abstract This paper is devoted to study interval-valued optimization p...

In these notes we review the role played by the quantum mechanics and sigma models of symmetric product spaces in the light-cone quantization of quantum field theories, string theory and matrix theory. Based on lectures given among others at the Geometry and Duality Workshop at the Institute for Theoretical Physics, UC Santa Barbara, January 1998 and the Spring School on String Theory and Mathe...